Remark 3.2 Note that the requirements on \(\beta \)  and \(\gamma \)  in Theorem REF  allow for the choice \(\beta =1/5\)  and \(\gamma =2/5<1/2\) . This yields the classical convergence rate \(n^{-2/5}\)  for series estimation with polynomials if the true density is sufficiently smooth (cf. [1]} and Proposition 3.6 in [2]}).

